The present invention relates generally to coordinate determination using satellite signals, and more particularly to coordinate determination using one-shot code coordinates and increments of carrier phase coordinates of satellite signals.
Satellite positioning systems, such as GPS (USA) and GLONASS (Russia), are well known in the art and are intended for highly accurate self-positioning of users possessing special navigation receivers. A navigation receiver receives and processes radio signals transmitted by satellites located within line-of-sight distance of the receivers. The satellite signals comprise carrier signals that are modulated by pseudo-random binary codes. The receiver measures the time delay of the received signal relative to a local reference clock or oscillator. These measurements enable the receiver to determine the so-called pseudo-ranges between the receiver and the satellites. The pseudo-ranges are different from the ranges (distances) between the receiver and the satellites due to various noise sources and variations in the time scales of the satellites and receiver. If the number of satellites is large enough, then the measured pseudo-ranges can be processed to determine the user location, i.e. code coordinates, and coordinate time scales. This type of system uses a single satellite receiver and is referred to herein as a stand alone system. These stand alone systems typically provide meter-level accuracy.
The requirement of determining user location with a high degree of precision, and the desire to improve the stability and reliability of measurements, have led to the development of differential navigation (DN). In differential navigation, the task of finding the user position, also called the Rover, is performed relative to a Base station (Base). The precise coordinates of the Base station are known and the Base station is generally stationary during measurements. The Base station has a navigation receiver which receives and processes the signals of the satellites to generate measurements. These signal measurements are transmitted to the Rover via a communication channel (e.g., wireless). The Rover uses these measurements received from the Base, along with its own measurements taken with its own navigation receiver, in order to precisely determine its location. The location determination is improved in the differential navigation mode because the Rover is able to use the Base station measurements in order to compensate for the major part of the strongly correlated errors in the Rover measurements. DN mode based on measuring pseudo-ranges only is called Differential Global Positioning Service (DGPS).
Various modes of operation are possible while using differential navigation. In post-processing (PP) mode, the Rover's coordinates are determined by co-processing the Base and Rover measurements after all measurements have been completed. This allows for highly accurate location determination because more data is available for the location determination. In real-time processing (RTP) mode, the Rover's coordinates are determined in real time upon receipt of the Base station information received via the communication channel.
The location determination accuracy of differential navigation may be further improved by supplementing the pseudo-range measurements with measurements of the phases of the satellite carrier signals. If the carrier phase of the signal received from a satellite in the Base receiver is measured and compared to the carrier phase of the same satellite measured in the Rover receiver, measurement accuracy may be obtained to within several percent of the carrier's wavelength. Real-time carrier signal based differential navigation is often referred to as real-time kinematic (RTK). The practical implementation of these advantages, which might otherwise be guaranteed by the measurement of the carrier phases, runs into the problem of ambiguity resolution for phase measurements.
The ambiguities are caused by two factors. First, the difference of distances from any satellite to the Base and Rover is usually much greater than the carrier's wavelength. Therefore, the difference in the phase delays of a carrier signal received by the Base and Rover receivers may substantially exceed one cycle. Second, it is not possible to measure the integer number of cycles from the incoming satellite signals; one can only measure the fractional part. Therefore, it is necessary to determine the integer number of cycles, which is called the “ambiguity”. More precisely, the set of all such integer parts for all the satellites being tracked, one integer part for each satellite, needs to be determined. One has to determine this set along with other unknown values, which include the Rover's coordinates and the variations in the time scales.
At a high level, the task of generating highly-accurate navigation measurements is formulated as follows: it is necessary to determine the state vector of a system, with the vector containing nΣ unknown components. Those include three Rover coordinates (usually along Cartesian axes X, Y, Z) in a given coordinate system (sometimes time derivatives of coordinates are added too); the variations of the time scales which is caused by the phase drift of the local main reference oscillator in the receiver; and n integer unknown values associated with the ambiguities of the phase measurements of the carrier frequencies. The value of n is determined by the number of different carrier signals being processed, and accordingly coincides with the number of satellite channels actively functioning in the receiver. At least one satellite channel is used for each satellite whose broadcast signals are being received and processed by the receiver. Some satellites broadcast more than one code-modulated carrier signal, such as a GPS satellite which broadcasts a carrier in the L1 frequency band and a carrier in the L2 frequency band. If the receiver processes the carrier signals in both of the L1 and L2 bands (i.e., a dual-frequency receiver), the number of satellite channels (n) increases correspondingly. Dual-frequency receivers allow for ionosphere delay correction and make ambiguity resolution easier.
Two sets of navigation parameters are measured by the Base and Rover receivers, respectively, and are used to determine the unknown state vector. Each set of parameters includes the pseudo-range of each satellite to the receiver, and the full (complete) phase of each satellite carrier signal. Each pseudo-range is obtained by measuring the time delay of a code modulation signal of the corresponding satellite. The code modulation signal is tracked by a delay-lock loop (DLL) circuit in each satellite tracking channel. The full phase of a satellite's carrier signal is tracked by a phase-lock-loop (PLL) in the corresponding satellite tracking channel. An observation vector is generated as the collection of the measured navigation parameters for specific (definite) moments of time.
The relationship between the state vector and the observation vector is defined by a well-known system of navigation equations. Given an observation vector, the system of equations may be solved to find the state vector if the number of equations equals or exceeds the number of unknowns in the state vector. Conventional statistical methods are used to solve the system of equations: the least squares method, the method of dynamic Kalman filtering, and various modifications of these methods.
Practical implementations of these methods in digital form may vary widely. In implementing or developing such a method on a processor, one usually must find a compromise between the accuracy of the results and speed of obtaining results for a given amount of processor capability, while not exceeding a certain amount of loading on the processor.
One specific type of abnormal error is a phase lock loop (PLL) cycle slip. A PLL cycle slip is a cycle slip in the PLL circuits that are tracking the satellite carrier signal. After a cycle slip occurs, the PLL circuit transits to a new point of steady balance, after which it goes on with tracking the satellite carrier signal. As a result of a cycle slip, an abnormal error equal to several integer numbers of semi-cycles (half-cycles) is introduced into the full phase measurements. A cycle slip is characterized by two parameters: value and duration. The slip's value (in cycles) is determined by either 0.5K or K dependent on the PLL discriminator's type, where K is a random integer number. The duration of the cycle slip is also random. Minimal duration is defined by the PLL band while maximal duration depends upon the cause bringing about the cycle slip and can last up to several seconds. When the duration is long enough, tracking is lost.
Much of the advancements in satellite positioning has been directed to suppressing various types of errors. Differential navigation, for example, mitigates errors caused by the atmosphere, inaccurate knowledge of satellite trajectory, and the drift of a satellite's onboard clock. Other techniques have been developed to reduce the influence of abnormal errors, such as by analyzing indicators of anomalies. These techniques detect and eliminate incorrect and inaccurate measurements, such as when the parameters of received signals are degraded by heavy interference. There are also techniques of analyzing observation results which allow for redundancy of the satellite number to isolate a few unreliable measurements.
The US government has stopped the intentional degradation of the GPS signals (also referred to as Selective Availability). As a result, a new generation of navigational receivers has been and continues to be designed and developed. A typical aim of these receivers is to determine relative rover motion with regard to its initial position (i.e., its local coordinates). The initial point (origin) of local coordinates originates from a marked point on the ground. Code coordinates or carrier phase increments can be used to measure rover position. Note that using carrier phase increments typically provides more accurate coordinates.
When considering the use of the above technologies, there is a trade-off between accuracy and cost. The most accurate technique is RTK, which can generally provide centimeter-level accuracy. However, this mode of operation requires a Rover and Base station both having a dual-frequency receiver, a radio for communicating corrections from the Base to the Rover via a communication link, and an algorithm for solving the ambiguities of the carrier phase measurements. Thus, while providing accurate positioning results, this mode of operation is also the most expensive, in terms of equipment costs, processing power, and complexity.
Alternatively, the least accurate technique is the stand alone system described above, which provides only meter-level accuracy. While less accurate, this type of system is also the least expensive and least complex, as it requires only a single satellite receiver and no base station.
RTK-receivers cannot traditionally operate in complex environments (for instance, in woods) when satellite signals are shaded and strong reflected signals have phases that change rapidly during rover movement. This results in large errors and a failure of RTK to resolve ambiguities and obtain fixed solutions. Further, using discrete code-modulated pseudo-range samples is also often inaccurate.
To improve the situation for single-frequency and/or standalone receivers, smoothing the measured pseudo-ranges with full carrier phases can be performed. Most pseudo-range errors are related to noise-induced fast fluctuations and multipath errors (when the rover is moving). Multipath errors also change quickly due to phase shifts. Pseudo-range fast fluctuations can be smoothed by a filter. However, this filter must not substantially increase dynamic errors. A Kalman filter, as well as a number of other filters with constant parameters, can be employed for smoothing. The results of heavy filtering depend on motion dynamics. For the Kalman filter, a priori data on dynamics parameters is to be specified in the motion model. Traditionally, the more complex the model is, the lower the accuracy achieved.
The measured carrier phase contains information about changes in the relative “satellite-observer” distance (i.e., the distance between a satellite and an observer), which also includes the rover's dynamics. As a result, combining code and phase measurements often considerably reduces the degree of uncertainty and enhances the efficiency of filtering.
Cycle slips often prevent the carrier phase from being continuously used. Continuous carrier phase refers to a known initial point from which phase increments are integrated in such a way that the stored number of full cycles (even if it is not observable at any given moment in time) is correctly considered. If a signal is weak or lost, the integration result is incorrect and highly affects the phase cycle integers, thereby degrading the results of filtering.